12bis. Mixture of logit with panel data and segmented ASC

Variant of the panel mixed logit example where one ASC is segmented using the socio-economic variable MALE. This can be used to reproduce the panel renaming issue if shared Variable objects are renamed multiple times.

Michel Bierlaire, EPFL

from IPython.core.display_functions import display

See the data processing script swissmetro_panel.py.

from swissmetro_panel import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    MALE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    database,
)

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta, Draws, MonteCarlo, PanelLikelihoodTrajectory, log
from biogeme.models import logit
from biogeme.results_processing import (
    EstimationResults,
    get_pandas_estimated_parameters,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info("Example b12_panel_segmented_male.py")

Parameters to be estimated.

b_cost = Beta("b_cost", 0, None, 0, 0)

Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation.

b_time = Beta("b_time", 0, None, 0, 0)

It is advised not to use 0 as starting value for the following parameter.

b_time_s = Beta("b_time_s", 1, 1.0e-5, None, 0)
b_time_rnd = b_time + b_time_s * Draws("b_time_rnd", "NORMAL_ANTI")

Random ASCs to address serial correlation.

asc_car = Beta("asc_car", 0, None, None, 0)
asc_car_s = Beta("asc_car_s", 1, 1.0e-5, None, 0)
asc_car_rnd = asc_car + asc_car_s * Draws("asc_car_rnd", "NORMAL_ANTI")

asc_train = Beta("asc_train", 0, None, None, 0)
asc_train_s = Beta("asc_train_s", 1, 1.0e-5, None, 0)
asc_train_rnd = asc_train + asc_train_s * Draws("asc_train_rnd", "NORMAL_ANTI")

asc_sm = Beta("asc_sm", 0, None, None, 0)
asc_sm_s = Beta("asc_sm_s", 1, 1.0e-5, None, 0)
asc_sm_rnd_base = asc_sm + asc_sm_s * Draws("asc_sm_rnd", "NORMAL_ANTI")

Segmentation of one ASC by the socioeconomic variable MALE. This is intentionally written in a way that reuses the same variable in a comparison expression, to reproduce the original issue.

asc_sm_male = Beta("asc_sm_male", 0, None, None, 0)
asc_sm_rnd = asc_sm_rnd_base + asc_sm_male * (MALE == 1)

asc_train_male = Beta("asc_train_male", 0, None, None, 0)
asc_sm_male = Beta("asc_sm_male", 0, None, None, 0)
asc_car_male = Beta("asc_car_male", 0, None, None, 0)

v_train = (
    asc_train_rnd
    + asc_train_male * (MALE == 1)
    + b_time_rnd * TRAIN_TT_SCALED
    + b_cost * TRAIN_COST_SCALED
)

v_swissmetro = (
    asc_sm_rnd_base
    + asc_sm_male * (MALE == 1)
    + b_time_rnd * SM_TT_SCALED
    + b_cost * SM_COST_SCALED
)

v_car = (
    asc_car_rnd
    + asc_car_male * (MALE == 1)
    + b_time_rnd * CAR_TT_SCALED
    + b_cost * CAR_CO_SCALED
)

Associate utility functions with the numbering of alternatives.

v = {1: v_train, 2: v_swissmetro, 3: v_car}

Associate the availability conditions with the alternatives.

av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}

Conditional on the random parameters, the likelihood of one observation is given by the logit model (called the kernel).

choice_probability_one_observation = logit(v, av, CHOICE)

Conditional on the random parameters, the likelihood of all observations for one individual (the trajectory) is the product of the likelihood of each observation.

conditional_trajectory_probability = PanelLikelihoodTrajectory(
    choice_probability_one_observation
)

We integrate over the random parameters using Monte-Carlo.

log_probability = log(MonteCarlo(conditional_trajectory_probability))

the_biogeme = BIOGEME(
    database,
    log_probability,
    number_of_draws=5_000,
    seed=1223,
    calculating_second_derivatives="never",
)
the_biogeme.model_name = "b12_panel_segmented_male"

Estimate the parameters.

try:
    results = EstimationResults.from_yaml_file(
        filename=f"saved_results/{the_biogeme.model_name}.yaml"
    )
except FileNotFoundError:
    results = the_biogeme.estimate()

print(results.short_summary())

pandas_results = get_pandas_estimated_parameters(estimation_results=results)
display(pandas_results)

List of columns of the flat database generated by Biogeme.

for col in the_biogeme.model_elements.database.dataframe.columns:
    print(col)

List of variables that have been renamed in the model specification.

for var in the_biogeme.model_elements.expressions_registry.variables:
    print(var)